Question

Resolva o sistema
3x + 5y = 11
2x + 2y = 5

Answer 1

Resolva o sistema

{3x + 5y = 11
{2x + 2y = 5

$x = \frac{11}{3} - \frac{5}{3} y \\ \\ 2x + 2y = 5 \\ \\ \\ 2( \frac{11}{3} - \frac{5}{3} y) + 2y = 5 \\ \\ \frac{22}{3} - \frac{4y}{3} = 15 \\ \\ - 4y = 15 - 22 \\ \\ - 4y = - 7 \\ \\ y = \frac{7}{4} \\ \\ 2x + 2 \times \frac{7}{4} = 5 \\ \\ x = \frac{3}{4} \\ \\ (x \: \: y) = ( \frac{3}{4} \: \: \frac{7}{4} )$

Answer 2

Olá

vamos resolver por comparação 

3x + 5y = 11
2x + 2y = 5 

isola x em ambas as equações..

$3x=11\;-\;5y\\ \\ x= \frac{11\;-\;5y}{3} \\ \\ 2x=5\;-\;2y\\ \\ x= \frac{5\;-\;2y}{2}$

 x = x 

$\frac{11\;-\;5y}{3} = \frac{5\;-\;2y}{2} \\ \\ multiplica\;cruzado\\ \\ 2(11\;-\;5y)=3(5\;-\;2y)\\ \\ 22\;-\;10y=15\;-\;6y\\ \\ 22\;-\;15=-\;6y\;+\;10y\\ \\ 7\;=\;4y\\ \\ y= \frac{7}{4} \\ \\ 2x\;+\;2y=5\\ \\ 2x\;+\;2.( \frac{7}{4} )=5\\ \\ 2x= 5 \;-\; \frac{7}{2} \\ \\ 2x= \frac{3}{2} \\ \\ x= \frac{3}{2} * \frac{1}{2} \\ \\ x = \frac{3}{4}$

S = {$\frac{3}{4} ,\; \frac{7}{4}$}

$Bons\;estudos!$